Added Riesz.

src/topology/main/index.tex

@@ -16,5 +16,6 @@
 \input{./src/topology/main/compact.tex}
 \input{./src/topology/main/sigma-compact.tex}
 \input{./src/topology/main/para.tex}
+\input{./src/topology/main/support.tex}
 \input{./src/topology/main/lch.tex}
 \input{./src/topology/main/baire.tex}

src/topology/main/support.tex

@@ -0,0 +1,17 @@
+\section{Support}
+\label{section:topology-support}
+
+\begin{definition}[Support]
+\label{definition:support}
+    Let $X$ be a topological space, $E$ be a TVS over $K \in \RC$, and $f \in C(X; E)$, then $\supp{f} = \ol{\bracs{f \ne 0}}$ is the \textbf{support} of $f$.
+\end{definition}
+
+\begin{definition}[Compactly Supported]
+\label{definition:compactly-supported}
+    Let $X$ be a topological space, $E$ be a TVS over $K \in \RC$, and $f \in C(X; E)$, then $f$ is \textbf{compactly supported} if $\supp{f}$ is compact. The set $C_c(X; E)$ is the vector space of all $E$-valued compactly supported functions on $X$.
+\end{definition}
+
+\begin{definition}
+\label{definition:compactly-supported-01}
+    Let $X$ be a topological space, $f \in C_c(X; [0, 1])$ and $U \subset X$ be open, then $f \prec U$ if $\supp{f} \subset U$
+\end{definition}